Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the covering dimension of subspaces of product of Sorgenfrey lines


Author: Ali A. Fora
Journal: Proc. Amer. Math. Soc. 72 (1978), 601-606
MSC: Primary 54F45
DOI: https://doi.org/10.1090/S0002-9939-1978-0509262-1
MathSciNet review: 509262
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let S denote the Sorgenfrey line. Then the following results are proved in this paper:

(i) If X is a nonempty subspace of $ {S^{{\aleph _0}}}$, then $ \dim X = 0$.

(ii) For any nonempty separable space $ X \subset {S^{{\aleph _0}}},\dim {X^m} = 0$ for any cardinal m.


References [Enhancements On Off] (What's this?)

  • [E] R. Engelking, Outline of general topology, North-Holland, Amsterdam, 1968. MR 0230273 (37:5836)
  • [G] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, New York, 1960. MR 0116199 (22:6994)
  • [I] J. R. Isbell, Uniform spaces, Math. Surveys, American Mathematical Society, Providence, R.I., 1964. MR 0170323 (30:561)
  • [Mr1] S. Mrowka, Recent results on E-compact spaces and structures of continuous functions (Proc. Univ. of Oklahoma Topology Conf., 1972), Univ. of Oklahoma, Norman, 1972, pp. 168-221. MR 0358693 (50:11152)
  • [Mr2] -, Recent results on E-compact spaces, TOPO-General Topology and its Applications, Lecture Notes in Math., vol. 378, Springer, Berlin and New York, 1974, 298-301. MR 0362231 (50:14673)
  • [P] T. C. Przymusiński, On the dimension of product spaces and an example of M. Wage (to appear).
  • [Ta] H. P. Tan, Doctoral Dissertation, Buffalo University, 1973.
  • [Te1] J. Terasawa, On the zero-dimensionality of some nonnormal product spaces, Sci. Rep. Tokyo Kyoiku Daigaku 11 (1972), 167-174. MR 0310850 (46:9948)
  • [Te2] -, NUR and their dimensions (to appear).
  • [W] M. Wage, The dimension of product spaces (to appear). MR 507930 (80a:54064)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F45

Retrieve articles in all journals with MSC: 54F45


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0509262-1
Keywords: Completely regular, cozero cover, cozero set, N-compact, order of a cover, Tychonoff
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society